Generalized Symmetries in Quantum Field Theory and Quantum Gravity

量子场论和量子引力中的广义对称性

• 批准号: EP/X028291/1
• 负责人: Sakura Schafer-Nameki
• 金额: $ 274.53万
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FX028291%2F1
• 关键词: Generalized; Symmetries; Quantum; Field; Theory

Symmetries are one of the most fundamental concepts in physics, addressing some of the core questions, such as the phase structure of quantum systems, as well as the consistency of quantum gravity. The past few years have seen an unexpected explosion of what can comprise a symmetry of a quantum theory. Generalized notions of symmetry include higher-form symmetries, whose charged objects, in contrast to ordinary symmetries, are higher-dimensional (e.g. Wilson or 't Hooft line operators), higher-groups (which capture the interplay between higher-form symmetries) and, more generally, categorical symmetries, sub-system symmetries (which are localized, e.g. in fracton order) and non-invertible symmetries. These generalized symmetry structures have genuine physical implications: they provide order parameters for confinement in gauge theories, constrain renormalization group flows by 't Hooft anomalies, and characterize low di- mensional topological order. However, a complete theoretical framework has yet to emerge, and the full breadth of physical implications are yet to be explored. Given the central importance of symmetries, the main goal of this project is to provide a comprehensive characterization of these generalized symmetry structures, and to study their physical implications upon the vacuum structure of field theories. The project has two main tranches: half of the research group will work on field theoretic approaches, using insights from high energy and condensed matter physics. The second half will explore generalized symmetry structures in the context of strongly-coupled field theories from string theory, holography, as well as their implications in quantum gravity, such as extensions of the weak gravity gravity conjecture and completeness conjectures. The project will draw strongly from the synergy between higher energy physics, condensed matter, mathematics, and quantum gravity, to explore the physics of these new symmetries in quantum theory.

对称性是物理学中最基本的概念之一，解决了一些核心问题，例如量子系统的相结构，以及量子引力的一致性。在过去的几年里，量子理论的对称性发生了意想不到的爆炸。广义的对称性概念包括高阶对称性（higher-form symmetry），它的带电对象与普通对称性不同，是高维的（例如Wilson或't Hooft线算符）、高阶群（捕捉高阶对称性之间的相互作用），以及更一般的范畴对称性、子系统对称性（局部化的，例如分形序）和不可逆对称性。这些广义对称结构具有真正的物理意义：它们为规范理论中的约束提供序参量，通过t Hooft反常约束重整化群流，并表征低维拓扑序。然而，一个完整的理论框架尚未出现，物理影响的全部广度尚未被探索。鉴于对称性的核心重要性，这个项目的主要目标是提供这些广义对称结构的全面表征，并研究它们对场论真空结构的物理意义。该项目有两个主要部分：研究小组的一半将致力于场论方法，利用高能和凝聚态物理学的见解。下半部分将探讨广义对称结构的强耦合场理论的背景下，从弦理论，全息，以及它们的量子引力的影响，如弱重力引力猜想和完整性的扩展。该项目将强烈借鉴高能物理，凝聚态，数学和量子引力之间的协同作用，探索量子理论中这些新对称性的物理学。